Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Answer:2x^3
Step-by-step explanation:
10x^3-12x^3
2x^3(5-6)
Answer:
2 1/2
Step-by-step explanation:
If you do the step by step calculation:
Step 1: Simplify both sides of the equation.
2(12+2x+15+2x)=74
(2)(12)+(2)(2x)+(2)(15)+(2)(2x)=74(Distribute)
24+4x+30+4x=74
(4x+4x)+(24+30)=74(Combine Like Terms)
8x+54=74
8x+54=74
Step 2: Subtract 54 from both sides.
8x+54−54=74−54
8x=20
Step 3: Divide both sides by 8.
8x divide by 8 and that is 20 divided by 8
leaves you with the answer 5/2.
If you then turn the improper fraction into a mixed fraction you get 2 and one half.
Answer= 2 1/2 or "a" <u>DEPENDS ON WHAT QUIZ YOU HAVE</u>
Peace!
Answer:
Surface area = 10.7 in.²
Step-by-step explanation:
Surface Area of triangular pyramid = BA + P*L
Base Area (BA) = ½*nh
b = 2 in.
h = 1.7 in.
BA = ½*2*1.7 = 1.7 in.²
Perimeter (P) = 2 + 2 + 2 = 6 in.
Slant height (L) = 3 in.
Plug in the values
Surface Area = 1.7 + ½*6*3
Surface area = 10.7 in.²
